Given the function f'(x) = x^5 + 20x^4, determine all intervals on which f is decreasing.

Question

SnapAndSolve AI · Accepted Answer

To determine where the function f is decreasing, we need to find where f'(x) < 0.

Given f'(x) = x^5 + 20x^4, factor the expression:

f'(x) = x^4(x + 20).

Set f'(x) < 0:

Since x^4 is always non-negative (as it is an even power), the inequality depends on (x + 20):

Thus, the function f is decreasing on the interval (-∞, -20).

Answer